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• Finite Element Flux-Corrected Transport (FEM-FCT) for the Euler and Navier-Stokes equations

  R. Lohner, K. Morgan, J. Peraire, M. Vahdati

  International Journal for Numerical Methods in Fluids (1987). Vol. 7 (10), pp. 356-361

  
  

  Abstract

  A high resolution finite element method for the solution of problems involving high speed compressible flows is presented. The method uses the concepts of flux-corrected transport and is presented in a form which is suitable for implementation on completely unstructured triangular or tetrahedral meshes. Transient and steady state examples are solved to illustrate the performance of the algorithm.

  Abstract
  A high resolution finite element method for the solution of problems involving high speed compressible flows is presented. The method uses the concepts of flux-corrected transport [...]

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• Some useful data structure for generation of unstructured grid

  R. Lohner

  Communications in numerical methods in engineering (1988). Vol. 4 (1), pp. 123-135

  
  

  Abstract

  Several data structures for the generation of unstructured grids are described. Their usefulness stems from the fact that they enable the necessary search operations to be performed in an optimal way. In particular, we describe heap lists, quad- and octrees, and linked lists. Combining these data structures, the important problem of interpolating information between unstructured grids is also solved.

  Abstract
  Several data structures for the generation of unstructured grids are described. Their usefulness stems from the fact that they enable the necessary search operations to be [...]

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• Numerical simulation of shock-box interaction using an adaptive shock capturing scheme

  J. Baum, R. Lohner

  AIAA Journal (1988). Vol. 32 (4), pp. 682-690

  
  

  Abstract

  A recently developed transient, two-dimensional, finite-element shock capturing scheme is applied to the study of shock interaction with a box suspended above a rigid surface. The results demonstrate the excellent resolution of the captured shocks and the application of a newly developed adaptive refinement/coarsening algorithm. In addition to interesting shock propagation and interaction processes, the results demonstrate the capability of the new code to capture, and define in great detail, vortices shed from the downstream corners of the box. The ability of the new scheme to model such fluid dynamic phenomena as shock-shock, shock-surface, and shock-vortex interactions, as well as vortex dynamics, are demonstrated.

  Abstract
  A recently developed transient, two-dimensional, finite-element shock capturing scheme is applied to the study of shock interaction with a box suspended above a rigid surface. [...]

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• Adaptive Finite Element Flux Corrected Transport Techniques for CFD

  K. Morgan, J. Peraire, R. Lohner

  (1988). Finite Elements. ICASE/NASA LaRC Series. Springer, New York, NY

  
  

  Abstract

  In previous papers [1,2] we have described an explicit finite element solution procedure for the compressible Euler and Navier-Stokes equations. The approach was a finite element equivalent of a two-step Lax-Wendroff scheme and was implemented on unstructured triangular or tetrahedral grids. An important feature of the work was the use of adaptive mesh refinement methods for the solution of steady state problems in two dimensions, using error indicators based upon interpolation theory.  

  Abstract
  In previous papers [1,2] we have described an explicit finite element solution procedure for the compressible Euler and Navier-Stokes equations. The approach was a finite [...]

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• Generation of three-dimensional unstructured grids by the advancing-front method

  R. Lohner, P. Parikh

  International Journal for Numerical Methods in Fluids (1988). Vol. 8 (10), pp. 1135-1149

  
  

  Abstract

  The generation of three-dimensional unstructured grids using the advancing-front technique is described. This technique has been shown to be effective for the generation of unstructured grids in two dimensions.1,2 However, its extension to three-dimensional regions required algorithms to define the surface and suitable data structures that avoid excessive CPU-time overheads for the search operations involved. After obtaining an initial triangulation of the surfaces, tetrahedra are generated by successively deleting faces from the generation front. Details of the grid generation algorithm are given, together with examples and timings.

  Abstract
  The generation of three-dimensional unstructured grids using the advancing-front technique is described. This technique has been shown to be effective for the generation [...]

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• An adaptive finite element solver for transient problems with moving bodies

  R. Lohner

  Computers and Structures (1988). Vol. 30 (1-2), pp. 303-317

  
  

  Abstract

  The combination of adaptive remeshing techniques, flow solvers for transient problems with moving grids, and integrators for rigid body motion is presented. The resulting scheme allows the economic simulation of fully coupled fluid-rigid body interaction problems of arbitrary geometric complexity. Several results are given to demonstrate the capabilities developed.

  Abstract
  The combination of adaptive remeshing techniques, flow solvers for transient problems with moving grids, and integrators for rigid body motion is presented. The resulting [...]

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• FEM-FCT - Combining unstructured grids with high resolution

  R. Lohner, K. Morgan, M. Vahdati, J. Boris, D. Book

  Communications in numerical methods in engineering (1988). Vol. 4 (6), pp. 356-370

  
  

  Abstract

  We present the extension of flux‐corrected transport (FCT) schemes to unstructured grids. The spatial discretization is performed via finite elements. In particular, we have chosen triangular elements in two dimensions. The limiting procedure is based on Zalesak's extension to more than one dimension of the FCT schemes developed by Boris and Book. The resulting scheme, FEM‐FCT, is capable of resolving moving and stationary shocks within two elements, and several examples are given that demonstrate the accuracy attainable, even for complicated geometries.

  Abstract
  We present the extension of flux‐corrected transport (FCT) schemes to unstructured grids. The spatial discretization is performed via finite elements. In particular, [...]

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• Adaptive remeshing for transient problems

  R. Lohner

  Computer Methods in Applied Mechanics and Engineering (1989). Vol. 75 (1-3), pp. 195-214

  
  

  Abstract

  Adaptive remeshing schemes for transient problems are presented. The main advantage of these schemes is the ease in incorporating directional refinement and body motion in the context of adaptive refinement. Practical numerical examples for the Euler equations, run on the CRAY-XMP-24 at NRL, show that the adaptive remeshing scheme by itself cannot compete with ordinary h-refinement for strongly unsteady flows that require a grid change every 5–10 timesteps. Therefore, we study the combination of adaptive remeshing and h-refinement. After generating a coarser grid with stretched elements, the whole grid is h-refined at once. Even with one level of h-refinement, the combined scheme easily out-performs ordinary h-refinement, yielding a very effective adaptive refinement method for this class of problems.

  Abstract
  Adaptive remeshing schemes for transient problems are presented. The main advantage of these schemes is the ease in incorporating directional refinement and body motion [...]

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• A vectorized particle tracer for unstructured grids

  R. Lohner, J. Ambrosiano

  Journal of Computational Physics (1990). Vol. 91 (1), pp. 22-31

  
  

  Abstract

  A vectorized particle tracer for unstructured grids is described. The basic approach is to use elementary properties of the linear basis functions to search for particles on the grid using the element last occupied as an initial guess. To permit vectorization, a simple binary sort of the particles is performed every timestep such that all particles that have as yet not found their host element remain at the top of the list. In this way, vector-loops can be easily formed. Timings taken from a numerical example indicate that speed-ups of the order of 1:14 can be obtained on vector-machines when using this algorithm.

  Abstract
  A vectorized particle tracer for unstructured grids is described. The basic approach is to use elementary properties of the linear basis functions to search for particles [...]

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• Numerical simulation of shock interaction with complex geometry canisters

  J. Baum, E. Loth, R. Lohner

  (1990). AIP Conference Proceedings, vol. 209

  
  

  Abstract

  The objective of this research is to investigate shock interaction with complex geometry canisters suspended above a rigid elevated surface. Several geometries were examined in an effort to reduce the loads on the canisters during the shock diffraction phase. A new transient, two‐dimensional, finite‐element shock capturing scheme was utilized. Excellent shock resolution was demonstrated, as well as the efficiency of the newly developed adaptive refinement/coarsening algorithm. In addition to interesting shock wave propagation and interaction processes, the results demonstrated the capability of the new code to capture, and define in great detail, vortices shed from the downstream side of the canister.

  Abstract
  The objective of this research is to investigate shock interaction with complex geometry canisters suspended above a rigid elevated [...]

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